Abstract
The study of a stochastic optimal control problem with feedback control leads us to a deterministic optimal control problem governed by a Kolmogorov equation with open-loop control. We analyse the relationship between the stochastic and the deterministic optimal control problems. We show the existence of an optimal control in a particular case, derive the optimality conditions for the deterministic problem and translate these results to the stochastic problem. Additional comments and further extensions are discussed. Some auxiliary results are also given.
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